Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations

Pavol Brunovský, Romain Joly, Geneviève Raugel

In this paper, we consider the scalar reaction-diffusion equations ${\partial }_{t}u=\Delta u+f(x,u,\nabla u)$ on a bounded domain $\Omega \subset {\mathbb{R}}^d$ of class $C^2$. We show that the h…